Assume my time value is \$0. High gas heat adds more energy per second to the water but the pot may absorb the heat less efficiently, or maybe the shape of the flame is less good, or for other reasons diminishing returns are encountered. Low enough gas heat might never boil the water. Is there an efficient optimum in the middle that uses the least total gas to get the water to 100℃?
More generally: what are the factors in a real-life situation of warming something up that differ from the simplest model of a knob that makes "temperature" rise (characterises the entire fluid by one scalar), forgetting that something physical has to heat up something else physical?